Infrared Gas Heater

ABSTRACT

The invention is directed to an infrared gas heater for a building, comprising: 
     a first straight energy emitter tube; a U-shaped energy emitter tube connect to said first straight, energy emitter tube; a second straight, energy emitter tube having and end connected to said U-shaped energy emitter tube; a reflector system for reflecting heat energy toward the floor of a building; a frame having rollers mounted thereon, said rollers for supporting said first and second straight, energy emitter tubes; a gas heating source connected to the first straight, energy emitter tube at the end opposite the U-shaped energy emitter tube; and whereby the second straight, energy emitter tube at the end opposite the U-shaped energy emitter tube is a gas exhaust.

FIELD OF THE INVENTION

The present invention relates to the field of infrared gas heaters employed to heat large enclosed space such as a warehouse, gymnasium, aircraft hanger, commercial applications such as retail stores, or agriculture buildings for raising chicken or turkey indoors, etc. The infrared heater of the present invention comprises a U-shaped tube and dual straight tubes with energy input at one end and exhaust at the other end. The key features are asymmetric double reflectors over the dual straight tubes, a symmetric reflector over the asymmetric double reflectors, placement of flow restrictors within the tubes at the U-shaped tube end of the heater, and rollers supporting the dual straight tubes before and after the U-shaped tube. Other features will also be known from the following disclosure.

PRIOR ART

Infrared gas heaters are known. They are available in many shapes such as a single tube, a U-shaped tube having dual straight tubes, multiple U shapes, and an L configuration. The key goal for all infrared heaters is to deliver more radiant heat energy to the floor level of a building to maintain the themial mass on the floor level and to obtain quicker recovery when doors at the floor level are opened and closed frequently. A repeatable testing method documented in Standard EN416-2 has been developed to test the efficiency of the infrared heaters. Infrared heaters produce radiant heat energy, convection heat energy, and heat energy that stems from products of combustion that are exhausted outside the building, sometimes referred to as flue gas. As stated above the key goal is to maximize the radiant heat energy and maintain it at floor level. Current emphasis of consumer demand of heating products that use fossil fuels is to minimize the impacts on the environment by reducing the overall energy consumption and therefore reducing the CO₂ (carbon dioxide) emissions. The invention disclosed in this application are new methods of construction specifically relevant to a radiant heater which is high efficiency and reduces overall the CO₂ (carbon dioxide) emissions for the operation of a building heating system.

This invention is directed to U-shaped tube with dual straight tubes, where 2 pieces of straight tube are connected to a U-shaped tube. Typical construction are for an energy input at one end and an exhaust at the other end or energy input and combustion air at the same end. The known U-shaped tube with dual straight tubes may include a flow restrictor which is installed in the exhaust end to recover heat energy just before it is exhausted.

There are many problems with U-shaped tube with dual straight tubes infrared heaters. First the dual tubes have different expansion rates due to the heat energy differences in both tubes. The tubes therefore have to be able to expand and contract independently. If they are restricted from freedom to expand and contract then the force of the expansion induced by the higher operating temperatures of a high efficiency heater may cause any or all of the following issues; bowing of the emitter tubes, distortion of the suspension brackets, or distortion of the reflectors. Second, the heat energy inlet tube also heats the exhaust tube. This is acerbated by the flow restrictor at the exhaust end where the back pressure slightly slows the gas flow rate allowing the heat energy inlet tube more time to transfer heat to the exhaust gas. Therefore energy efficiency is lost at this point. Typical reflectors above the dual tubes reflect the heat down and back onto the tubes. This causes the heat energy to be concentrated on the dual tubes heater thereby blocking some heat from getting to the floor level. The heat energy is not widely distributed when the reflectors bounce the heat back on the tubes. This is another loss in efficiency. Standard infrared gas heaters having a U-shaped tube with dual straight tubes typically transfer 50% of the heat energy to the floor level by radiant energy and another 27% by convection heat energy. This means about 23% is exhaust flue gas. The exhaust is also another point of loss efficiency.

Thus there is a need to reduce the consumption of fossil fuels by improving the energy efficiency of infrared heaters having a U-shaped tube with dual straight tubes. These and other problems are overcome with the present invention.

The radiant heat output from a body can be calculated as Q=Fε F_(G) σ A (T₁ ⁴−T₂ ⁴).

Radiant Output Q is expressed in Btu/hr/ft².

Fε is the emissivity function where a black body is equal to 1.0 and all other surfaces are less than 1.0. In the case of radiant tube heaters this is the emissivity of the emitter tubes used to radiate the heat to the receiver.

F_(G) is the geometric view factor defined as how well the receiver can “see” the energy being transmitted in the infrared wavelength from the source.

σ is the Stefan Boltzmann constant 0.1714×10⁻⁸ BTU/Hr⁻¹ Ft³¹ ² R⁻⁴

A is the surface area of the heat source which is the emitter tubes.

T₁ ⁴−T₂ ⁴ is the absolute temperature of the heat source to the power of four minus the absolute temperature of the receiver to the power of 4. In terms of radiant heat energy transmission, increasing the surface area of the source by as much temperature/heat energy as possible is the critical multiplier to increase the overall radiant output.

SUMMARY OF THE INVENTION

In the broadest sense, the present invention is directed to an infrared gas heater for a building, comprising:

-   -   a first straight energy emitter tube;     -   a U-shaped energy emitter tube connect to said first straight,         energy emitter tube;     -   a second straight, energy emitter tube having an end connected         to said U-shaped energy emitter tube;     -   a flow restrictor within the energy tube in close proximity to         the U-shaped emitter tube;     -   a reflector system for reflecting heat energy toward the floor         of a building;     -   a frame having rollers mounted thereon, said rollers for         supporting said first and second straight, energy emitter tubes;     -   a gas heating source connected to the first straight, energy         emitter tube at the end opposite the U-shaped energy emitter         tube; and     -   whereby the second straight, energy emitter tube at the end         opposite the U-shaped energy emitter tube is a gas exhaust.

In another broad sense, the present invention is directed to an infrared gas heater for a building, comprising:

-   -   a first straight energy emitter tube;     -   a U-shaped energy emitter tube connect to said first straight,         energy emitter tube;     -   a second straight, energy emitter tube having and end connected         to said U-shaped energy emitter tube;     -   a flow restrictor within the energy tube in close proximity to         the U-shaped emitter tube;     -   a reflector system for reflecting heat energy toward the floor         of a building;     -   a frame for mounting said first and second straight, energy         emitter tubes and said reflector system;     -   said reflector system includes one or more end plates extending         downwardly perpendicularly across each end of the first and         second straight, energy emitter tubes, said reflector system         also includes a lower pair of asymmetric downwardly directing         reflectors, one covering the top and sides of each straight,         energy emitter tube; said reflector system also includes an         upper symmetrical reflector covering the top and outsides of the         lower asymmetrical reflectors;     -   wherein said one or more end plates, said pair of lower         asymmetrical reflectors, and said upper symmetrical reflector         have bottom edges which are level with the bottom of said first         and second straight, energy emitter tubes, wherein the air space         between said upper and lower reflectors insulate the reflector         system to reduce convection losses from said lower reflectors         which increases the temperature around said energy emitter         tubes;     -   a gas heating source connected to the first straight, energy         emitter tube at the end opposite the U-shaped energy emitter         tube; and     -   whereby the second straight, energy emitter tube at the end         opposite the U-shaped energy emitter tube is a gas exhaust.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings are to aid in the understanding of the invention, but are not meant to limit the scope of the invention beyond the broad scope of the claims. While the drawing may show relative sizes of the components, it is also within the scope of the invention to realize that infrared gas heaters of the present invention can easily be produced in different sizes with different BTU outputs.

The present invention is illustrated and described herein with reference to the various drawings of exemplary embodiments, in which like reference numbers denote like system components, respectively, and in which:

FIG. 1 is an exploded, perspective view of infrared gas heater of the present invention.

FIG. 2 is a cross-sectional end view illustrating the shape of the asymmetrical reflectors as well as the symmetrical reflector.

FIG. 3 is an exploded partial view of just the U-shaped tube, the dual straight tubes and the flow restrictors that are within the dual straight tubes.

FIG. 4 is a cross sectional view illustrating the support of the dual straight tubes on rollers.

FIG. 5A is an end view of M-shaped asymmetric reflector 30.

FIG. 5B is an end view of M-shaped asymmetric reflector 28.

FIG. 5C is a perspective view illustrating the overlap of an asymmetrical reflector.

FIG. 6 is a graph of the efficiency of the present invention versus a standard infrared gas heater.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

While all the components of the infrared heater are commonly made of metal, the reflectors are constructed from highly reflective aluminum which has a reflectivity of about 96 to 99%. Other reflector materials such as aluminized steel or stainless steel have a reflectivity of about 80%, and stainless steel reflectors drops in reflectivity after 3 days of operation reducing the radiant efficiency by 3.1% due to discoloration from the heat. Gold plated metal has a reflectivity of about 99% but costs make it ridiculously expensive. Accordingly highly reflective aluminum is the best material for constructing the reflectors at a reasonable price. Aluminum reflectors are commonly used in the construction of radiant tube heaters where the reflectors are un-insulated, where the emitter tubes are substantially in close proximity to the reflectors the typical maximum temperature of aluminum reflectors arranged in single layer is 450° F., at this temperature the reflector material is still relatively strong and able to support its own weight without deformation. In the case that dual upper and lower aluminum reflectors are used the insulating effect of the upper reflector increases the lower reflector temperature to 750° F., this increase in temperature significantly reduces the strength of the aluminum reflector and increases the expansion which takes place. In order to maintain coverage of the emitter tubes along the length of the heater the aluminum reflectors must be overlapped and remain stable during expansion and contraction.

As illustrated in FIG. 1, the infrared heater 10, has dual straight emitter tubes 12 and 14 that are secured to the U-shaped emitter tube 16. These emitter tubes are typically made from high temperature material such as aluminized steel, stainless steel and titanium aluminum alloy coated steel to withstand the high temperatures of the heater. These emitter tubes are typically coupled together to form the shape shown in FIG. 1. The emitter tubes 12, 14, and 16 are supported on two or more cross supports 18. The number of cross supports employed depend on the length of the dual straight emitter tubes 12 and 14. Thus the size of the infrared heater can vary depending on the length and diameter of the emitter tubes. The longer the overall length, the more heat energy necessary to raise the temperature of the emitter tubes and therefore the gas heating source 20 can be made correspondingly bigger.

As shown in FIG. 1, three cross supports 18 a, 18 b and 18 c are present. The cross support 18 c adjacent the U-shaped emitter tube 16 has a U-shaped bolt and nut 22 which tightly secures one end of each of the dual straight tubes 12 and 14, and the U-shaped emitter tube 16 to one another, as shown in FIG. 2. The other cross supports 18 a and 18 b loosely support the dual straight tubes 12 and 14 because the U-shaped bolts and nuts 24 a and 24 b are not tightly securing the dual emitter tubes 12 and 14 to the corresponding cross supports 18 a and 18 b, as shown in FIG. 4. Since the gas heating source 20 is located at one end of straight emitter tube 12, it is plain to see that the emitter tube 12 will be hotter than emitter tube 14. Since the U-Shaped tube is secured tightly, the loose fit at all other points along the length of the emitter tubes 12 and 14 allows the dual tubes to expand (relative to the secured end) in a direction away from the U-shaped emitter tube 16 as they heat up during use. An 15 foot long straight emitter tube 12 expands almost ¾ inched longer than straight emitter tube 14. To aid in the different expansion rates, the cross supports 18 a and 18 b include rollers 26 as seen in FIG. 4 (shown only with respect to cross support 18 a, but 18 b is identical). The rollers 26 on cross supports 18 a and 18 b support the emitter tube 12 and another set of rollers 26 support the emitter tube 14. The rollers 26 allow the emitter tubes 12 and 14 to expand or contract relative to the secured cross support 18 c, where the dual straight emitter tubes 12 and 14 and the U-shaped emitter tube 16 are fixedly secure.

As shown in FIGS. 1 and 2, the dual straight emitter tubes 12 and 14 are covered lengthwise respectively by M-shaped asymmetric lower reflectors 28 and 30, as also shown in FIGS. 5A and 5B. The M-shaped lower reflectors 28 and 30 are spaced above the emitter tubes 12 and 14 and spaced above the U-shaped bolts 22. This prevents the reflectors 28 and 30 from distorting due to excessive temperature—especially lower reflector 28 which is positioned over the hotter emitter tube 12. The outside walls 32 of reflectors 28 and 30 are more horizontal than inside walls 34, thus making these lower reflectors asymmetric in shape. The M-shaped lower reflectors 28 and 30 reflect the radiant heat around the emitter tubes 12 and 14 to more fully direct and spread the radiant heat energy to the floor level. Further, each of the outside walls 32 and the inside walls 34 of lower reflectors 28 and 30 extend to about the bottom of each emitter tube 12 and 14. This arrangement insures that emitter tube 12 will not transfer heat energy to the exhaust emitter tube 14, especially just before the exhaust gas in emitter tube 14 exits the heater. Lastly the outside walls 32 spread the radiant heat energy toward the floor level in a larger pattern since the outside walls 32 are more horizontal than inside walls 34, as seen in FIGS. 5A and 5B. The vertical portion 36 of the cross supports 18 a,b,c as shown in FIG. 1 act to guide the outside walls 32 when they expand and contract independently from each other and the rest of the system. To guide the inside walls 34 during expansion and contraction, they are inserted into a T-shaped extrusion bar 38. The T-shaped extrusion bar 38 is positioned between, and extends the length of the emitter tubes 12 and 14. It is supported by and secured to the cross supports 18 a,b,c. To cover the length of the emitter tubes 12 and 14 with a reflector profile, M-shaped lower reflectors 28 and 30 overlap the next pair of M-shaped lower reflectors. As the preferred material is aluminum this overlap 58 as shown in FIG. 5C must allow the M-shaped lower reflectors to freely move, where if they are the same profile shown in FIG. 5A, they will become interlocked and the expansion during heating will result in distortion. To enable the M-shaped lower asymmetric reflectors to freely expand and contract without binding to each other a notch 56 is made in one end of both outside walls 32 and inside walls 34 of the M-shaped asymmetric reflectors. Thus the M-shaped lower asymmetric reflectors are supported but can still expand and contract independently from each other and from the emitter tubes 12 and 14 during heating and cooling.

As shown in FIG. 1, the U-shaped emitter tube 16 is covered by an inner reflector 40 which directs radiant heat energy downward to the floor level. Additionally a pair of end cap reflectors 42 and 44 prevents the radiant heat from escaping out the ends of the infrared heater. End cap 42 has a pair of upside down U-shaped holes 46 to allow for the emitter tubes 12 and 14 to slide (expand/contract) through the end cap and connect to the gas heating source 20 and the exhaust opening 48, which may include sufficient piping to exit beyond the interior of the building. Since the end cap reflectors 42 and 44 extend to the bottom of the emitter tubes 12 and 14, all the heat energy is retained to maintain a high temperature around the emitters and direct the heat energy downwardly.

Lastly a symmetrical upper reflector 50 is positioned above and around the M-shaped asymmetric lower reflectors 28 and 30 and the lower reflector 40 over and around the U-shaped emitter tube, as shown in FIGS. 1 and 2. This outer reflector is supported by brackets 52, which are secured to the M-shaped asymmetric lower reflectors 28 and 30, in a manner to create an insulation air gap 62 above and around the reflectors 28 and 30. Symmetrical upper reflector 50 traps convection heat between it and the asymmetrical reflectors 28 and 30 thereby preventing more convection heat escaping from the back of the asymmetric lower reflectors 28 and 30 which in turn maintains a higher emitter temperature along the length of the heater. This improves the overall efficiency of the infrared gas heater 10, because maintaining high emitter temperatures (source temperature T₁) over as much surface area of possible will give the most gain in radiant heat output. Typical material thickness of the M-shaped asymmetric lower aluminum reflectors 28 and 30 is 0.025″ to 0.032″. If thicker aluminum material or Rigidized® aluminum is used then physical insulation can be used in the air gap space 62 to reduce convection losses from the back of M-shaped asymmetric lower aluminum reflectors 28 and 30.

FIG. 3 illustrates the placement of flow restrictors 54 within the dual straight emitter tubes 12 and 14, near the end where these emitter tubes connect to the U-shaped emitter tube 16. Although any shape flow restrictor will work in the present invention, the bent, zigzag flow restrictors 54 work well. The flow restrictors cause a back pressure and turbulence within the emitter tubes 12 and 14, and create a bigger thermal mass in the area of the U-shaped emitter tube 16. This aids in exchanging more heat energy from the gas to the emitter tube and thus increasing the temperature of the emitter tubes 12 and 14 which in turn increases the measured radiant output in these sections.

In contrast thereto, the standard infrared gas heaters place the flow restrictors only in emitter tube 14 adjacent the exhaust 48. This propagates heat exchange between gas and the emitter tube 14 where the gas is significantly cooled and therefore does not have the same gain in emitter tube temperature. Additionally the exhaust gas is heated due to its proximity to the gas source 20 and more heat energy flows out the exhaust. This is clearly illustrated by FIG. 6. The solid line is a measure of the energy below the firing emitter tube 12, while the dashed line is a measure of the heat energy under the exhaust emitter tube 14. In the standard heater, the dashed line increases as it approaches the exhaust indicating an increase in heat energy just before the flue gas exits to the atmosphere. Contrarily for the present invention the solid line is highest at the gas source and tapers as it approached the U-shaped emitter tube 16. Then the two flow resistors 54 just before and just after the U-shaped emitter tube increase the heat energy due to the increased turbulence, back pressure and the thermal mass of the flow restrictors 54. Also note the height of the solid line at the gas source 20. The total area under this curve (of the dark line) is much larger that the total area under the curve of the standard heater. This means more energy is being transferred to the floor level and much less energy is escaping out the flue. In fact the temperature of the flue gas from the present invention is about half that of the standard heater. These two charts explain the key results obtained using the present invention. Moreover, the present invention heater known as the “NXU” was a 175,000 BTU heater and it was compared to a 200,000 BTU standard heater. Those skilled in the art would have readily anticipated that the NXU heater should have a much smaller area under the curve of the solid and dashed lines, than the standard heater solid and dashed areas under the curve for the higher BTU heater. Also the standard heater has a radiant energy at floor level of about 50%. On the other hand, the present invention as a radiant energy at floor level between 65 and 69%.

Further, note that the heated gas can either be pushed through the emitter tubes 12, 14, 16, or it can be pulled through the emitter tubes 12, 14, 16 depending merely on the position of the blower. As indicated via FIG. 1, the blower is associated with the gas heating source 20 and thus the gas is blown or pushed through the emitter tuber 12, 14, and 16. On the other hand, the exhaust 48 could contain the blower such that the gas in the emitter tubes 12, 14, 16 are pulled therethrough.

Thus it is apparent that there has been provided, in accordance with the invention, an improved infrared gas heater that fully satisfies the objects, aims and advantages set forth above. While the invention has been described in conjunction with specific embodiments thereof, it is evident that many alternatives, modifications, and variations will be apparent to those skilled in the art of radiant heaters with dual straight emitter tubes 12 and 14 and the U-shaped emitter tube 16 in light of the foregoing description. Accordingly, it is intended to embrace all such alternatives, modifications, and variations as fall within the spirit and broad scope of the appended claims 

What is claimed is:
 1. An infrared gas heater for heating a building, comprising: two straight, energy emitter tubes; a U-shaped energy emitter tube connect to one end of each of the two straight, energy emitter tubes; two lower reflectors, wherein one is positioned above each of said straight, energy emitter tubes; an upper reflector positioned above said two lower reflectors, thus creating an air space; a support frame for supporting said two straight, energy emitter tubes, said U-shaped energy emitter tube, said two lower reflectors, and said upper reflector; one flow restrictor, positioned within the energy emitter tube at the end adjacent the U-shaped energy emitter tube; two fasteners to securely position each of the straight, energy emitter tubes and each end of said U-shaped energy emitter tube on said frame; at least two rollers positioned on said frame, wherein at least one of said rollers support a straight, energy emitter tube, thus permitting each straight, energy emitter tube to expand and contract relative to said frame, to allow for different expansion and contraction rates; a gas heating source positioned adjacent one end of one of said straight, energy emitter tube opposite said U-shaped energy emitter tube; and an exhaust outlet at the other end of the other straight, energy emitter tube, opposite said U-shaped tube.
 2. The infrared gas heater of claim 1, wherein said lower reflectors are asymmetrical and shaped to reflect energy away from said straight, energy emitter tubes.
 3. The infrared gas heater of claim 2, wherein said asymmetrical lower reflectors are M-shaped in cross section, wherein a leg of the M-shaped cross section further away from a longitudinal center line of said frame is more horizontal than a leg of said asymmetrical reflector nearest said longitudinal center line.
 4. The infrared gas heater of claim 1, wherein said asymmetrical reflectors and said symmetrical reflector are constructed from aluminum having at least a 95% reflectance value.
 5. The infrared gas heater of claim 1, wherein said rollers are constructed of metal and can withstand the energy emitted from the straight, energy emitter tubes.
 6. The infrared gas heater of claim 1, wherein said lower reflectors are positioned to divert the energy emitted from the straight, energy emitter tubes from one another.
 7. The infrared gas heater of claim 3, wherein said frame includes a longitudinal metal holder to support a leg of each asymmetrical reflectors nearest said longitudinal center line, and said asymmetrical reflectors are notched to allow free expansion and contraction.
 8. The infrared gas heater of claim 1, wherein said asymmetrical reflectors enclose the top and sides of the straight, energy emitter tubes thus reflecting heat energy toward a floor of a building.
 9. The infrared gas heater of claim 8, wherein said symmetrical reflector encloses the top, and sides of said asymmetrical reflectors thus reflecting heat energy toward a floor of a building.
 10. The infrared heater of claim 1, wherein said air space is an insulating barrier to reduce convention loss.
 11. The infrared heater of claim 10, wherein said air space is filled with a physical insulation material.
 12. An infrared gas heater for a building, comprising: a first straight energy emitter tube; a U-shaped energy emitter tube connect to said first straight, energy emitter tube; a second straight, energy emitter tube having and end connected to said U-shaped energy emitter tube; a reflector system for reflecting heat energy toward the floor of a building; a frame having rollers mounted thereon, said rollers for supporting said first and second straight, energy emitter tubes; a gas heating source connected to the first straight, energy emitter tube at the end opposite the U-shaped energy emitter tube; and whereby the second straight, energy emitter tube at the end opposite the U-shaped energy emitter tube is a gas exhaust.
 13. The infrared gas heater of claim 12, wherein said reflector system includes one or more end plates extending downwardly perpendicularly across each end of the first and second straight, energy emitter tubes.
 14. The infrared gas heater of claim 13, wherein said reflector system also includes a pair of asymmetric downwardly directing reflectors, one covering the top and sides of each straight, energy emitter tube.
 15. The infrared gas heater of claim 14, wherein said reflector system also includes a symmetrical reflector covering the top and outsides of the asymmetrical reflectors, wherein said one or more end plates, said pair of asymmetrical reflectors, and said symmetrical reflector have bottom edges which are level with the bottom of said first and second straight, energy emitter tubes.
 16. The infrared gas heater of claim 12, wherein said rollers include at least 2 each of each straight, energy emitter tubes.
 17. The infrared gas heater of claim 12, wherein said frame reflector system is mounted on said frame.
 18. An infrared gas heater for a building, comprising: a first straight energy emitter tube; a U-shaped energy emitter tube connect to said first straight, energy emitter tube; a second straight, energy emitter tube having and end connected to said U-shaped energy emitter tube; a reflector system for reflecting heat energy toward the floor of a building; a frame for mounting said first and second straight, energy emitter tubes and said reflector system; said reflector system includes one or more end plates extending downwardly perpendicularly across each end of the first and second straight, energy emitter tubes, said reflector system also includes a pair of asymmetric downwardly directing reflectors, one covering the top and sides of each straight, energy emitter tube; said reflector system also includes a symmetrical reflector covering the top and outsides of the asymmetrical reflectors, thus creating an air space; wherein said one or more end plates, said pair of asymmetrical reflectors, and said symmetrical reflector have bottom edges which are level with the bottom of said first and second straight, energy emitter tubes; a gas heating source connected to the first straight, energy emitter tube at the end opposite the U-shaped energy emitter tube; and whereby the second straight, energy emitter tube at the end opposite the U-shaped energy emitter tube is a gas exhaust.
 19. The infrared gas heater of claim 18, whereby said bottom edges of said pair of asymmetric downwardly directing reflectors have a pair of bottom edges positioned adjacent one another.
 20. The infrared gas heater of claim 18, further comprising a longitudinal metal holder connect to said frame and positioned to receive said pair of bottom edges positioned adjacent one another and secure these pair of bottom edges with the frame. 